Determination of virtual item orientation based on its natural shape and proportion is a fundamental issue in a wide range of applications involving computer vision, robotics, biometrics, digital 3-D model database search, collision detection, pattern recognition, etc.
The Extended Gaussian Image (EGI) method for determining item orientation maps a plurality of surface normal vectors of an item onto a unit sphere in a way that the starting point of each normal vector is located at the center of the sphere and the end point on the surface of the sphere. The resulting area on the sphere spotted by the surface normals is known as a Gaussian map. Together with the end point a mass is placed which is equal to a local surface area where the normal is evaluated. From this a histogram of orientation is created and this histogram can be used to determine part orientation.
The EGI method works well for convex parts. If the parts are concave, however, different shapes may produce same or very similar EGI representation. In general, this method is suited for treating items described by a mesh type of representation, such as most Computer-Aided Engineering (CAE) mesh models made of finite elements. However, it can be applied to other representations as well with proper pre-processing. A Computer-Aided Design (CAD) surface, for instance, can be tessellated into a mesh before the method is applied, while a point cloud can be triangulated to a mesh first in order to apply it. One drawback of the EGI method, however, is its sensitivity to underlying mesh density and noise in the data.
Another statistical method which may be used to determine item orientation is Principal Component Analysis (PCA). PCA may be used to understand the contribution of variables to data distribution. It calculates uncorrelated linear combinations of data variables for which variances are maximized. PCA determines the principal components (direction) by solving for the Eigenvalues and Eigenvectors of co-variance matrix (inertia matrix). The principal direction vector with largest Eigenvalue gives a vector that has maximum co-variance and minimum deviation.
A drawback of PCA, when applied to models defined by meshes of nodes and elements, is that the results are tessellation-dependent because of sensitivity to mesh point distribution (density, evenness of spread, etc). For example, two finite element meshes derived from the same item model, but with different mesh node distribution characteristics, often yield different principal components. PCA, like EGI, is tessellation dependent yielding unstable or unreliable results.